Problem: Simplify the following expression: $ a = \dfrac{-8}{-10t + 4} + \dfrac{-7}{6} $
Explanation: In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{6}{6}$ $ \dfrac{-8}{-10t + 4} \times \dfrac{6}{6} = \dfrac{-48}{-60t + 24} $ Multiply the second expression by $\dfrac{-10t + 4}{-10t + 4}$ $ \dfrac{-7}{6} \times \dfrac{-10t + 4}{-10t + 4} = \dfrac{70t - 28}{-60t + 24} $ Therefore $ a = \dfrac{-48}{-60t + 24} + \dfrac{70t - 28}{-60t + 24} $ Now the expressions have the same denominator we can simply add the numerators: $a = \dfrac{-48 + 70t - 28}{-60t + 24} $ $a = \dfrac{70t - 76}{-60t + 24}$ Simplify the expression by dividing the numerator and denominator by -2: $a = \dfrac{-35t + 38}{30t - 12}$